On the m-torsion Subgroup of the Brauer Group of a Global Field

Details On the m-torsion Subgroup of the Brauer Group of a Global Field On the m-torsion Subgroup of the Brauer Group of a Global Field

2007-01-02

arxiv.org/abs/math/0701052v1

Mathematics

Number Theory

5 pages

Scientific paper

In this note, we give a short proof of the existence of certain abelian
extension over a given global field $K$. This result implies that for every
positive integer $m$, there exists an abelian extension $L/K$ of exponent $m$
such that the $m$-torsion subgroup of $\Br(K)$ equals $\Br(L/K)$.

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